Encyclopedia of Earthquake Engineering

2015 Edition
| Editors: Michael Beer, Ioannis A. Kougioumtzoglou, Edoardo Patelli, Siu-Kui Au

Stochastic Analysis of Nonlinear Systems

  • Annibale Luigi MaterazziEmail author
  • Marco Breccolotti
Reference work entry
DOI: https://doi.org/10.1007/978-3-642-35344-4_334


Earthquake engineering; Hysteresis; Nonlinearity; Random vibrations


The present chapter is devoted to the probabilistic analysis of the random response of nonlinear structural systems exposed to random excitation with special attention to earthquake action. The random system response may be due to random excitation, to random system properties, to random boundary conditions. The nonlinear character of the response is mainly due to the nonlinear materials properties and to the effect of large displacements (the so-called P-Δ effect).

The first pioneering studies on this topic took place in the 1960s and 1970s (VanMarcke et al. 1970; Iwan 1973; Atalik and Utku 1976; Spanos 1976), when equivalent linearization techniques were used, taking advantage of the availability of first digital computers.

The attention is limited herein to systems having deterministic properties, including deterministic boundary conditions, considering those types of nonlinearity that can...

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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringUniversity of PerugiaPerugiaItaly